Physics-informed deep learning for predicting optical properties of Nb–Ta anodic oxide films from spectroscopic ellipsometry

Abstract

The prediction of optical properties for anodic oxide films from spectroscopic ellipsometry data constitutes a typical inverse problem. Traditional iterative fitting methods suffer from high computational cost and strong dependence on the model structure. This study develops a physics-informed deep learning framework that addresses this challenge through two complementary modeling scenarios. At its core is a Fresnel-constrained neural network, which predicts optical constants (n, k) and ellipsometric parameters [tan(Ψ), cos(Δ)] using the two inputs of base metal composition and anodizing voltage. A hybrid loss function involving the Fresnel equations is employed to guarantee physical consistency with optical reflection rules, thus avoiding non-physical solutions. In addition, two complementary data-optimization strategies were introduced: wavelength selection and model-based data augmentation. The wavelength-selection strategy compresses the spectral input by retaining the most informative 200–350 nm region, while Gaussian-noise-enhanced synthetic samples are generated to expand the training dataset and reduce the risk of surrogate-model bias propagation. The integrated model exhibits good prediction accuracy, with test-set RMSE values of 0.090 for n and 0.038 for k. Notably, the model maintains its training and prediction efficiency even as the volume of data increases. These results show that embedding fundamental optical laws into a deep learning structure yields a robust and efficient framework. Together with targeted data-optimization strategies, this framework offers a promising avenue for the high-throughput inverse design and characterization of complex functional oxide systems.